Solve d^45774-8 - Socratic AI (ScanMath)

Question

Simplify the expression

5774 d^{4} - 8

Evaluate

d^{4} \times 5774 - 8

Solution

5774 d^{4} - 8

Show Solution

2 (2887 d^{4} - 4)

Evaluate

d^{4} \times 5774 - 8

Use the commutative property to reorder the terms

5774 d^{4} - 8

Solution

2 (2887 d^{4} - 4)

Show Solution

d_{1} = - \frac{4 4 \times 288 7 ^{3}}{2887}, d_{2} = \frac{4 4 \times 288 7 ^{3}}{2887}

Alternative Form

d_{1} \approx - 0.192932, d_{2} \approx 0.192932

Evaluate

d^{4} \times 5774 - 8

To find the roots of the expression,set the expression equal to 0

d^{4} \times 5774 - 8 = 0

Use the commutative property to reorder the terms

5774 d^{4} - 8 = 0

Move the constant to the right-hand side and change its sign

5774 d^{4} = 0 + 8

Removing 0 doesn't change the value,so remove it from the expression

5774 d^{4} = 8

Divide both sides

\frac{5774 d ^{4}}{5774} = \frac{8}{5774}

Divide the numbers

d^{4} = \frac{8}{5774}

Cancel out the common factor 2

d^{4} = \frac{4}{2887}

Take the root of both sides of the equation and remember to use both positive and negative roots

d = \pm 4 \frac{4}{2887}

Simplify the expression

More Steps

Evaluate

4 \frac{4}{2887}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 4}{4 2887}

Simplify the radical expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{2}{4 2887}

Multiply by the Conjugate

\frac{2 \times 4 288 7 ^{3}}{4 2887 \times 4 288 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

2 \times 4 288 7^{3}

Use n a = mn a^{m} to expand the expression

4 2^{2} \times 4 288 7^{3}

The product of roots with the same index is equal to the root of the product

4 2^{2} \times 288 7^{3}

Calculate the product

4 4 \times 288 7^{3}

\frac{4 4 \times 288 7 ^{3}}{4 2887 \times 4 288 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

42887 \times 4 288 7^{3}

The product of roots with the same index is equal to the root of the product

4 2887 \times 288 7^{3}

Calculate the product

4 288 7^{4}

Reduce the index of the radical and exponent with 4

2887

\frac{4 4 \times 288 7 ^{3}}{2887}

d = \pm \frac{4 4 \times 288 7 ^{3}}{2887}

Separate the equation into 2 possible cases

d = \frac{4 4 \times 288 7 ^{3}}{2887} d = - \frac{4 4 \times 288 7 ^{3}}{2887}

Solution

d_{1} = - \frac{4 4 \times 288 7 ^{3}}{2887}, d_{2} = \frac{4 4 \times 288 7 ^{3}}{2887}

Alternative Form

d_{1} \approx - 0.192932, d_{2} \approx 0.192932

Show Solution